login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A257024 Number of squares in the quarter-sum representation of n. 5
1, 1, 0, 1, 1, 2, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 1, 2, 1, 2, 0, 1, 0, 1, 1, 1, 2, 1, 2, 2, 0, 1, 0, 1, 1, 2, 1, 2, 1, 2, 2, 3, 0, 1, 0, 1, 1, 2, 0, 1, 2, 1, 2, 2, 3, 1, 0, 1, 0, 1, 1, 2, 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 2, 1, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,6
COMMENTS
Every positive integer is a sum of at most four distinct quarter squares; see A257019.
LINKS
EXAMPLE
Quarter-square representations:
r(5) = 4 + 1, so a(5) = 2;
r(11) = 9 + 2, so a(11) = 1;
r(35) = 30 + 4 + 1, so a(35) = 2.
MATHEMATICA
z = 100; b[n_] := Floor[(n + 1)^2/4]; bb = Table[b[n], {n, 0, 100}];
s[n_] := Table[b[n], {k, b[n + 1] - b[n]}];
h[1] = {1}; h[n_] := Join[h[n - 1], s[n]];
g = h[100]; Take[g, 100]; r[0] = {0};
r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, r[n - g[[n]]]]]
sq = Table[n^2, {n, 0, 1000}]; t = Table[r[n], {n, 0, z}]
u = Table[Length[Intersection[r[n], sq]], {n, 0, 250}]
CROSSREFS
Sequence in context: A054528 A025884 A352427 * A334996 A124433 A287104
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 15 2015
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 01:34 EDT 2024. Contains 370952 sequences. (Running on oeis4.)